In the figure below, given a
triangle ABC, BD is the median to AC, angle BCA = a
, and angle ABD = 90º 
a.
Prove that
x = a.
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FACTS AND HINTS:
Geometry problem solving is one of the most challenging skills for students to learn. When a
problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
